As you have observed I omitted Evariste Galois born on 25th October 1811 from my daily posts and this is because he is the one that influenced me to start the event ‘Celebrate Mathematicians in October‘ and so I decided to make a special post about him . First of all, I want to say that all the information from this post comes from the chapter ‘The life of Galois’ from the book ‘Galois Theory’ by Ian Stewart.
Evariste Galois was born near Paris on 25th October 1811. For his early education, his mom was in charge for educating him (concentrating more on the classics). In October 1823 he entered the lycee Louis-le-Grand, where he obtained first prize in Latin in the first years, and it’s also the time when he become interested in mathematics. He started ‘Elements de Geometrie’ by Legendre (a classic book that broke with the Euclidean tradition of school geometry) which he read ‘like a novel’ and mastered really quick. At this point his school texts were to easy and he turned to original memoirs of Lagrange and Abel. So at 15 years old, Galois was reading material for professional mathematicians. But he started to lose interest in his school subjects. Moreover, he seemed to work mostly in his head omitting parts of the solution. Without proper preparation he took the exam to enter Ecole Polytechnique, but he failed. ( Terquem editor of Nouvelles Annales des Mathematique said: “A candidate with superior intelligence is lost with an examiner of inferior intelligence.” ) In 1828 he entered Ecole Normale (a pale shadow of Ecole Polytechnique).
Galois’s first paper was on continued functions, but did not have anything special. Meanwhile, he was working on the theory of polynomial equations and submitted some of his results to the Academy of Science. At that time, the scientist in charge of this domain was Cauchy, who just published some paper on the behavior of functions under permutation of the variables. Unfortunately Cauchy rejected his papers and the manuscripts were lost. In 1829, his father committed suicide after a political dispute. In the same year, Galois tried for the second time to enter Ecole Polytechnique but failed again (the examiner asked him to outline the theory of ‘arithmetical logarithms’ and Galois said that there were no arithmetical logarithms, so the examiner failed him). In 1830, he submitted his research to Academy of Science for the competition for the Grant Prize in Mathematics. His paper was seen as a good one and reached the secretary Fourier. Unfortunately, Fourier died before he couldn’t read the paper and again Galois manuscripts disappeared. From all these problems, Galois started to believe that nothing was by chance. He saw them as ‘the effect of a society in which genius was condemned to an eternal denial of justice in favor of mediocrity’ and, obviously he stared to blame the political regime. This is the beginning of his fight against the political oppressive Bourbon regime.
In 1831, he tried to be a teacher of mathematics, offering a course in algebra, but he didn’t have success. He also submitted a paper called: On the conditions of solubility of equations by radicals. Cauchy was no longer in Paris and Poisson and Lacroix were named referees. Galois received no reply from them or the President of the Academy. After this, Galois joined the artillery of the National Guard, a Republican organization. He was arrested, but after trial he was set free. Unfortunately after this, Poisson declared his papers were ‘incomprehensible’. He stated:
We have made every effort to understand Galois’s proof. His reasoning is not sufficiently clear, sufficiently developed, for us to judge its correctness, and we can give no idea of it in this report. […] We would then suggest that the author should publish the while of his work in order to form a definitive opinion. but in the state which the part he has submitted to the Academy now is, we cannot propose to give it approval.
On 14 July, the same year, Galois was at the head of the Republican demonstration. He was imprisoned for 6 months after this. Due to the cholera epidemic of 1832 he was transferred to a hospital and after that put on parole.
With his freedom he experienced his first and only love affair. There is much mystery surrounding this story. Fragments of letters suggested that he was rejected that took it badly. Not long after this, he was challenged to a duel because of the relationship with the girl. Again, the circumstances are veiled in mystery (some consider this was a political move, others consider it to be just a love-duel). Galois words on this matter are:
Oh! why die for so trivial a thing, for something so despicable!… Pardon for those who have killed me, they are of good faith.
The duel took place on 30th May, Galois was hit in the stomach and died a day later. He refused the office of a priest, and on 2nd June he was buried in the common ditch at the cemetery of Montparnasse.
On 29th May, Galois wrote to his friend Auguste Chevalier outlining his discoveries. In this letter he sketched the connection between groups and polynomial equations, stating that an equation is soluble by radicals provided its group is soluble; he also mentioned other ideas about elliptic functions and the integration of algebraic functions. His letter ended with this words:
Ask Jacobi or Gauss publicly to give their opinion, not as to the truth, but as to the importance of these theorems. Later there will be, I hope, some people who will find it to their advantage to decipher all this mess…
It seemed that in the end other found ‘all this mess’ to be extremely useful and important. The modern approach to Galois theory was developed by Richard Dedekind, Leopold Kronecker and Emil Artin, among others. And now, in my last year of university I am studding Galois Theory. I hope that he is happy to see all the things are happening now because of his genius.
Thank you for your support and cooperation so far! (check the other related posts: Celebrate Mathematicians part 1, Celebrate Mathematicians part 2 and Celebrate Mathematicians part 3). Let me know what are your thoughts about Galois’s short life.
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